What does the graph of lnx^2 look like?

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SUMMARY

The discussion centers on the graph of the function \(\ln x^2\), which is confirmed to be the same as \(2\ln x\). Participants clarify that understanding the graph of \(\ln x\) is essential, as it serves as a foundation for graphing \(\ln x^2\). Key characteristics such as domain, asymptotes, intervals of increase/decrease, local minima/maxima, concavity, and inflection points are acknowledged, but the challenge lies in the actual graphing process without graphing calculators. The relationship between \(\ln x\) and \(e^x\) is also highlighted, emphasizing their inverse nature.

PREREQUISITES
  • Understanding of logarithmic functions, specifically \(\ln x\)
  • Familiarity with the properties of inverse functions, particularly \(e^x\)
  • Knowledge of graphing techniques for functions
  • Basic calculus concepts including local extrema and concavity
NEXT STEPS
  • Study the graph of \(\ln x\) to understand its shape and characteristics
  • Learn how to graph transformations of logarithmic functions, specifically \(y = a\ln x\)
  • Explore the relationship between logarithmic and exponential functions
  • Practice graphing functions using software tools like Desmos or GeoGebra
USEFUL FOR

Students, educators, and anyone interested in mastering the graphing of logarithmic functions and their transformations.

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what does the graph of lnx^2 look like?
 
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Is that \ln x^{2} ot (\ln x)^{2} ??If so,why don't u graph it??Do u know how??

Daniel.
 
it is lnx^2 (the first one) and i can't graph it. i don't know how. I've found all of the info ex. domain, asymptotes,intervals of increase/decrease, local min/max, concavity, and Inflection points

i can do those steps but have difficulty graphing functions

(and no graphing calc to check solutions)
 
If you know what \ln x looks like, you can easily graph \ln x^2, since \ln x^2=2\ln x.

If you don't know what \ln x looks like, it's the graph of e^x when mirrored through the line y=x, because they are the inverse functions of each other.

If you don't know what e^x looks like..., well you should.
 
i do...but is it lnx just stretched by 2?
 
thankx you!
 

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